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Advanced Physics
Chegg experts gave the wrong answer the last time I asked this, so I am asking it again. Please only answer if you know how to solve the problem!
Consider a directed graph G = (V, E) having a source vertex s and sink vertex t. Suppose that it has positive integer edge capacities c_e for all edges in the graph. Also suppose that is has a flow f = {f(e)} for all edges in the graph. We consider an edge to be saturated if f(e) = c_e.
Suppose that f is a maximum s-t flow. Let S represent the set of all saturated edges. Consider the minimum total capacity of any given s-t cut. Will it be equal to the total capacity of S? If true, please provide a proof. Otherwise, if it is false, give a counterexample.
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